Tensegrity twisted prism in 3D, using SageMath

tensegrity.py

# Tensegrity twisted prism. PM 2Ring 2024.08.31

def ball(radius, **kwargs):
    var('u,v')
    kw = dict(plot_points=40) | kwargs
    return spherical_plot3d(radius, (u, 0, 2*pi), (v, 0, pi), **kw)

def axis_matrix(W):
    a, b, c = W
    if abs(c) == 1:
        return identity_matrix(3) * sgn(c)
    U = vector([b, -a, 0]).normalized()
    V = W.cross_product(U)
    return matrix([U, V, W]).T

def cyl(V0, V1, radius=1, **kwargs):
   W = V1 - V0
   wnorm = W.norm()
   M = axis_matrix(W / wnorm)
   func = V0 + M * vector([radius * cos(u), radius * sin(u), v])
   kw = dict(plot_points=(40, 2)) | kwargs
   return parametric_plot3d(func, (u, 0, 2*pi), (v, 0, wnorm), **kw)

def circ(q):
    sn, cs = n(2 * pi * q).sincos()
    return vector((cs, sn, 0))

@interact
def main(num=3, twist=1/3,
  height=3.0r, c_rad=0.10r, t_rad=0.05r,
  c_color="#0a0", t_color="#b00",
  dark=True, perspective=True, auto_update=False):

    Z = vector((0, 0, height))
    pos_lo = [circ(i / num) for i in range(num)]
    pos_hi = [circ((i + twist) / num) + Z for i in range(num)]

    P = Graphics()
    b = ball(radius=c_rad, color=c_color)
    P += sum(b.translate(p) for p in pos_lo + pos_hi)

    P += sum(cyl(*pq, radius=t_rad, color=t_color)
      for pq in zip(pos_lo, pos_lo[1:]+pos_lo[:1]))
    P += sum(cyl(*pq, radius=t_rad, color=t_color)
      for pq in zip(pos_hi, pos_hi[1:]+pos_hi[:1]))

    P += sum(cyl(*pq, radius=t_rad, color=t_color)
      for pq in zip(pos_lo, pos_hi))

    P += sum(cyl(*pq, radius=c_rad, color=c_color)
      for pq in zip(pos_lo, pos_hi[1:]+pos_hi[:1]))

    theme = "dark" if dark else "light"
    projection = "perspective" if perspective else "orthographic"
    kw = dict(frame=False, theme=theme, projection=projection, online=True)
    P.show(**kw)
    P.save("tensegrity.html", **kw)

Live version on SageMathCell